On 17 Dec 2013, at 19:55, meekerdb wrote:
On 12/17/2013 1:51 AM, Bruno Marchal wrote:
On 17 Dec 2013, at 02:03, meekerdb wrote:
On 12/16/2013 4:41 PM, LizR wrote:
On 17 December 2013 13:07, meekerdb <meeke...@verizon.net> wrote:
In a sense, one can be more certain about arithmetical reality
than the physical reality. An evil demon could be responsible
for our belief in atoms, and stars, and photons, etc., but it is
may be impossible for that same demon to give us the experience
of factoring 7 in to two integers besides 1 and 7.
But that's because we made up 1 and 7 and the defintion of
factoring. They're our language and that's why we have control
of them.
If it's just something we made up, where does the "unreasonable
effectiveness" come from? (Bearing in mind that most of the non-
elementary maths that has been found to apply to physics was
"made up" with no idea that it mighe turn out to have physical
applications.)
I'm not sure your premise is true. Calculus was certainly
invented to apply to physics. Turing's machine was invented with
the physical process of computation in mind.
Absolutely not. The "physical" shape of the Turing machine was only
there for pedagogical purpose.
Are you denying that Turing wanted to reason about realizable
computation??
Yes. When working on the foundation of math (not when working on
Enigma).
Of course his reasoning itself was abstract and led to a
mathematical theorem. But Liz was asking about the unreasonable
effectiveness of mathematics. I don't think you can say that
Turing, or Babbage or Post or Church just became interested in
sequences of symbol manipulation because they dreamed about it.
They were trying to find solutions to paradox arising arousing around
Cantor set theory.
They were concerned with real instances of inference and
calculation, from which they abstracted recursive functions and
Turing machines.
It is the contrary. Like Gödel discovered the primituve recursive
functions, and miss Church thesis, just when working on Hilbert's
problem (to find an elementary consistent proof of a set theory). Same
for Post, Church, Turing, and the others.
In fact I got problem when saying to a mathematician that the work of
Gödel, Church, and Turing was relevant to computer science. Such work
were classified as pure mathematics, with no applications possible
(sic).
the discovery of universal machine is a purely mathematical, even
arithmetical, discovery. "physical implementation" came later (if
you except Babbage, but even Babbage will discover the mathematical
machine (and be close to Church thesis), when he realized that his
functional description language (intended at first as a tool for
describing his machine) was a bigger discovery than his machine.
The discovery of the universal machine is the bigger even discovery
made by nature. It is even bigger than the big bang. And nature
exploit it all the time, and with comp we understand completely why.
I agree with the first sentence. I don't understand the second.
Don't mind too much. We can come back to this later. I see most events
in the physical universe as apparition of universal systems, including
the big bang. But then that is how arithmetic has to look like from
inside, when we assume comp.
That discovery is a theorem of elementary arithmetic, and has
nothing to do with the physical, except that with comp, we get the
explanation of the physical as a consequence of that theorem in
arithmetic.
Non-euclidean geometry of curved spaces was invented before
Einstein needed it, but it was motivated by considering
coordinates on curved surfaces like the Earth. Fourier invented
his transforms to solve heat transfer problems. Hilbert space was
an extension of vector space in countably infinite dimensions. So
the 'unreasonable effectiveness' may be an illusion based on a
selection effect.
This beg the question, of both the existence of math, and of a
primitive physical reality (and of the link between).
So what's your answer to Wigner?
Math works because the fundamental reality is mathematical. The
physical reality emerge as a persistent first person sharable sort of
arithmetical video game.
Is it just an accident that the math the universe instantiates,
You assume some primitive universe. But there is no evidence at all,
and on the contrary, the simplest explanation (number's dream) does
not allow it to exist in any reasonable sense.
out of all mathematical universes Tegmark contemplates, happens to
use the same math we discovered?
Tegmark forgets to sum on all first person experience/computation-
viewed from inside. The physical reality is made conceptually very
solid in the comp theory. It is lawful and stable. But that physical
reality is only the border of a much vaster reality, that a machine
cannot distinguish from arithmetic seen from inside.
Bruno
Brent
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